I don't know exactly where you are starting from, but you can work your way over to Highway 27 in the western part of the state. You can take 80 from Macon to Columbus and then north from there, or you can work your way over further south.

From Waycross I would head over to Albany, then up Hwy 82/520 to Columbus. From Columbus go up I-185 and get on Hwy 27 just south of LaGrange. Take Hwy 27 from LaGrange through Carrollton stay on Hwy 27 and go past Cedartown then through Rome and get in the park from Hwy 27. Lots of 4 lane road. I think the main entrance to the park is off of Hwy 27. Or you could take GA Hwy 100 from Cedartown to Summerville and go SE on Hwy 27 for 3 miles to the entrance. About the only city traffic you will have is in LaGrange, Carrollton and Rome, which should not be a problem. Through Columbus you will be on Interstate Hwy. No need to go near Atlanta.